Epilepsy diagnosis through visual examination of interictal epileptiform discharges (IEDs) in scalp electroencephalogram (EEG) signals is a challenging problem. Deep learning methods can be an automated way to perform this task. In this work, we present a new approach based on convolutional neural network (CNN) to detect IEDs from EEGs automatically. The input to CNN is a combination of raw EEG and frequency sub-bands, namely delta, theta, alpha and, beta arranged as a vector for one-dimensional (1D) CNN or matrix for two-dimensional (2D) CNN. The proposed method is evaluated on 554 scalp EEGs. The database consists of 18,164 IEDs marked by two neurologists. Five-fold cross-validation was performed to assess the IED detectors. The resulting 1D CNN based IED detector with multiple sub-bands achieved a false positive rate per minute of 0.23 and a precision of 0.79 at 90% sensitivity. Further, the proposed system is evaluated on datasets from three other clinics, and the features extracted from CNN outputs could significantly discriminate (p-values <; 0.05) the EEGs with and without IEDs. We have proposed an optimized method with better performance than the literature that could aid clinicians to diagnose epilepsy expeditiously, and thereby devise proper treatment.